The owner of the car with an N53 series engine from the Czech Republic approached me. Sometimes the car takes a long time to start. Typically it happens, when the car has been turned off for at least one hour. Additionally, the problem appears exactly in cases if the warmed-up engine is left turned off. If the cold engine is left turned off, the problem is not observed.
The standard diagnostics didn’t indicate anything suspicious. The injectors were not leaking; the fuel mixture at the moment of start was correct.
Then I asked to send a video with the oil pressure menu.

0:02 the engine is started. As we see, the oil pressure for 2 seconds stays almost 0 hPa, not considering that the engine reaches 400 RPM.
0:04 the oil pressure suddenly swiftly increases, DME checks the max oil pressure (it reaches above 7 bar), then the pressure drops, and the DME starts to maintain the required value (2600 .. 3200 hPa, depending on the engine temperature).
Here, video with the PWM of the oil pressure regulation valve.

0:03 the Start/Stop button is pressed
0:06 the engine starts
As you see, the PWM of the valve is 0 for a longer time, which means: the valve is closed, and the oil pump works on full power. When the minimal pressure by which the DME allows to start the engine is reached, the engine is started. Then DME tests max pressure, which the oil pump can develop. As soon as the max pressure is confirmed, the PWM of the valve increases rapidly – the valve is opened, and the oil pressure is reduced to the necessary (required by DME) value.
In my evaluation – a typical situation, if the oil from the contour flows down to the oil pan, the longer time is necessary to pump it up again. All symptoms of the defect confirm exactly this defect. If the oil is hot and liquid – it flows down to the oil pan. Cold oil does not leak to the oil pan (obviously, the leak is small), and the defect is not observed. The oil backflow valve (it is located below the oil filter) and other valves should be checked in this situation.
The owner went to the specialized BMW service center, where the diagnosis was swiftly defined. All injectors and the HPFP pump should be replaced. The estimate (bill): around 3000 EUR.
What was the justification for such a verdict? The Rail pressure is dropping too fast. Here is the data:
Time 13:24 – engine off (warm) – pressure150000 hPa
Time 13:42 – 137750 hPa
Time 13:47 – 116900 hPa
Time 13:53 – 96250 hPa
Time 13:55 – 84850 hPa
Time 14:00 – 28900 hPa
Time 14:04 – 5000 hPa
Time 14:08 – 4500 hPa
Time 14:15 – 40000 hPa
Time 14:25 – 2500 hPa
Some reservations now takes place:
a. using ISTA, the fuel system test is performed for 30 seconds (in addition – only low-pressure is measured, not Rail pressure). The BMW service center performed the test for a minute, which means 2 times longer. After 30 seconds, the Rail pressure is around 100 bar;
b. the HPFP is not perfect, and it is also not its task. It is only logical that when it does not work, the fuel flows back in LP contour. According to my experience – typically, Rail pressure drops till LP pressure during several tens of seconds – several minutes. In this case, the result (100 bar after 30 seconds) does not indicate increased fuel leakage. Even engines, to which the Rail pressure drops for 90% during 4 .. 5 seconds, have no problem starting!
c. N43/N53 series engines are correctly starting with significantly reduced Rail pressure and even completely turned off HPFP. This is not a diesel engine, which requires the appropriate Rail pressure! N43/N53 starts in Homogeneous injection mode, and it has no problems, even if the Rail pressure is only 5000 hPa (5 bar) – as, for example, N52. Even more – such 5 bar Rail pressure is used if DME has identified increased fuel consumption from Rail (obviously, some injector is strongly leaking, or HPFP is damaged).
Obviously, the BMW service center specialists are not familiar with anything of this. But this does not prevent from suggesting to replace all the expensive parts and issue the bill for several thousand EUR. It is needless to say that they don’t even detect and identify any problems with the oil pressure.
In this case, even the elementary logic failed the specialists. If the Rail pressure drops practically to 0 during one minute, why the problem appears only in case the car was switched off for 50 times longer? Even if we assume that during that time, all fuel from the engine leaks out (the air gets in the system, and that is the cause of the long start), the leakage prevention needs to be started with the LP system, not injectors and HPFP!